A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility

In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with general mobility. The proposed fully-discrete scheme is carefully constructed based on combination of first backward differentiation formulas nonuniform time steps temporal approximation central finite difference spatial discretization. discrete maximum bound principle proved by using kernel recombination technique under certain mild constraints ratios adjacent step sizes. Furthermore, rigorously derive H 1 H^{1} error estimate energy stability classic constant mobility case L normal infinity"> L ∞ encoding="application/x-tex">L^{\infty } case. Various experiments are also presented to validate theoretical results demonstrate performance adaptive strategy.